Contour Method: Calculating Stress Using Finite Elements

Principle:

Make Cut

Measure Surface

Calculate Stress

Build finite element model of cut part No need to model actual deformed shape - displacements are small Shown here in 2-D, build 3-D model to get full cross-sectional stress map
Take opposite of measured contour Because we need to force deformed shape back to flat
Apply to finite element model Apply to edge of model as displacement boundary conditions Apply in normal direction only, leave other directions unconstrained
Extract results Post-process finite element results to get stress along edge where boundary conditions were applied

Now we have the residual stresses that originally existed normal to the plane of the cut! Illustrated here for just a 1-D stress profile, but see Applications for examples of getting a full 2-D stress map.